Numerical Modeling of Material Discontinuity Using Mixed MLPG Collocation Method B. Jalušić 1 , J. Sorić 1 and T. Jarak 1 Abstract A mixed MLPG collocation method is applied for the modeling of material discontinuity in heterogeneous materials composing of homogeneous domains. Two homogeneous isotropic materials with different linear elastic properties are considered. The solution for the entire domain is obtained by enforcing the corresponding continuity conditions along the interface of homogeneous materials. For the approximation of the unknown field variables MLS functions with interpolatory conditions are applied. The accuracy and numerical efficiency of the mixed approach is compared with a standard primal meshless approach and demonstrated by a representative numerical example. Keywords: Mixed meshless approach, MLS approximation, heterogeneous materials 1 Introduction In recent decades, a new group of numerical approaches known as meshless methods has attracted tremendous interest due to its potential to overcome certain shortcomings of mesh-based methods such as element distortion problems and time-demanding mesh generation process. Nevertheless, the calculation of meshless approximation functions due to its high computational cost is still a major drawback. This deficiency can be alleviated to a certain extent by using the mixed Meshless Local Petrov-Galerkin (MLPG) Method paradigm [Atluri, Liu, Han (2006)]. In the present contribution, the MLPG formulation based on the mixed approach is adapted for the modeling of deformation responses of heterogeneous materials. A heterogeneous structure consists of two homogeneous materials which are discretized by grid points in which equilibrium equations are imposed. The linear elastic boundary value problem for each homogeneous material is discretized by using the independent approximations of displacement and stress components. Independent variables are approximated using meshless functions in such a way that each material is treated as a separate problem [Chen, Wang, Hu, Chi (2009)]. The global solution for the entire heterogeneous structure is acquired by enforcing appropriate displacement and traction conditions along the interface of two homogeneous materials. A collocation meshless method is used, which may be considered as a special case of the MLPG approach, where the Dirac delta function is utilized as the test function. Since the collocation method is 1 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia.